Gondor and the Éothéod had been friends and allies in the past, when the Men of the Éothéod dwelt further to the south, but since their move into the north few messengers had passed between the two realms. Nonetheless Eorl agreed to Cirion's desperate request, and he gathered almost his entire force into a great éoherë consisting of some seven thousand horsemen, and a few hundred archers. Taking Borondir as a guide, the Ride of Eorl set out to cover the hundreds of miles into the south. The Ride proceeded from Framsburg through the eastern Vales of Anduin. As they approached the southern parts of Mirkwood, they kept as far to the west as they could to avoid the darkness of Dol Guldur, and Galadriel sent a white mist across the Great River to protect them as they passed her land.2

Notes

1

Though the general course of Eorl's Ride is well documented, his final approach to the Field of Celebrant is a little uncertain. We're told that he crossed the Undeeps, then the Limlight, to reach his destination. That seems to imply that he crossed the shallows of Anduin (presumably at the North Undeep), then turned back northwards to cross the Limlight.

This is corroborated by much of what we know of the battle itself. A counterattacking army from Gondor had been forced northwards by the invaders, and was trapped against the Anduin when Eorl attacked from the south, surprising the enemy from the rear and relieving the beleaguered Gondorians.

This concept of the battle fits well with all the evidence we have, except for a reference in Unfinished Tales where we're told that '...the Riders came out of the North and broke upon the rear of the enemy.' (in Cirion and Eorl, our italics). All other indications suggest that Eorl's riders made their attack from the south, so this reference to their coming 'out of the North' is presumably a general reference to Eorl's entire journey, rather than describing the specific events of the battle.

2

In fact it's never said explicitly that Galadriel sent the shining mist that aided the Ride, but this was Borondir's assumption. Given that the strange mist definitely originated from Lórien, and drove back the shadows of Dol Guldur so that the riders could pass, it does appear that Borondir's guess must have been correct.